Problem 52125. Compute the sum of reciprocals of quadratics

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.008px 7.79167px; transform-origin: 143.008px 7.79167px; unicode-bidi: normal; "><span style="">Write a function to compute the following sum:</span></span></div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="y = sum(1/(n^2+an+b),{n,1,infinity})" style="width: 122.5px; height: 45px;" width="122.5" height="45"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.175px 7.79167px; transform-origin: 29.175px 7.79167px; unicode-bidi: normal; "><span style="">See also </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers"><span style=""><span style="text-decoration: underline; text-decoration-line: underline; ">Cody Problem 46000</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

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Last Solution submitted on Oct 28, 2022

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Nikolaos Nikolaou on 30 Jul 2021

Thought this works only when both roots are negative

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Problem 52125. Compute the sum of reciprocals of quadratics

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Problem 52125. Compute the sum of reciprocals of quadratics

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